Problem: Simplify the following expression: $x = \dfrac{-96r - 24}{-24r - 12}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-96r - 24 = - (2\cdot2\cdot2\cdot2\cdot2\cdot3 \cdot r) - (2\cdot2\cdot2\cdot3)$ The denominator can be factored: $-24r - 12 = - (2\cdot2\cdot2\cdot3 \cdot r) - (2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $x = \dfrac{(12)(-8r - 2)}{(12)(-2r - 1)}$ Dividing both the numerator and denominator by $12$ gives: $x = \dfrac{-8r - 2}{-2r - 1}$